A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
نویسندگان
چکیده
منابع مشابه
A Numerical Bifurcation Function for Homoclinic Orbits
We present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of X.-B. Lin and solutions of the adjoint variational equation, we get a bifurcation function for periodic orbits whose period is asymptotic to innnity on approaching a homoclinic orbit. As a bonus, a linear predictor for continuation of the homoclinic orbit is easily available. Numerical approximatio...
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We consider a bifurcation of a flow in three dimensions from a double homoclinic connection to a fixed point satisfying a resonance condition between the eigenvalues. For correctly chosen parameters in the unfolding, we prove that there is a transitive attractor of Lorenz type. In particular we show the existence of a bifurcation to an attractor of Lorenz type which is semiorientable, i.e., ori...
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An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical “blow-up” technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit firstand second-order corrections of the unperturbed homoclinic orbit and parameter value. To ob...
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PREFACE Computational applications generally involve nonlinear problems and often contain parameters. They may represent properties of the physical system they describe or quantities which can be varied. A basic problem in approximation consists in studying existence and convergence of approximated solutions for a given nonlinear problem, for instance when the parameters are xed. Another proble...
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One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-do...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 1996
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127496000485